Let us call 
the probability, for a person of age x and in
status j at time 0, of being in status k at time t.
can be obtained by solving the
``forward Kolmogorov equations'', which decompose interval 
into 
and 
.
Introducing the 4 transition forces:
one can write for example:
These 6 differential equations can also be written (8):
with :
Last equations, involving 
have been suppressed
for simplicity. Two of the four equations are redundant, because
. The system can
therefore clearly be reduced
to a set of two first order differential equations involving four
forces and submatrix :
